What is the most general definition of "intelligence"?
I'm going to preface this answer by noting that persons much smarter than myself have treated this subject in some detail.  That said, as far as I can discern:

When we talk about intelligence we're referring to problem solving strength in relation to a problem, relative to the strength of other intelligences.

This is a somewhat game-theoretic conception, related to rationality and the concept of the rational agent.  Regarding intelligence in this manner may be unavoidable. Specifically, we could define intelligence as the ability to understand a problem or solution or abstract concepts, but we can't validate that understanding without testing it.  (For instance, I might believe I grasp a mathematical technique, but the only way to determine if that belief is real or illusory is to utilize that technique and evaluate the results.)
The reason games like Chess and Go have been used as milestones, aside from longstanding human interest in the games, is that they provide models with simple, fully definable parameters, and, in the case of Go at least, have complexity akin to nature, by which I mean unsolvable/intractable. (Compare to strength at Tic-Tac-Toe, which is trivially solved.)
However, we should consider a point made in this concise answer to a question involving the Turing Test:

&quot;...is [intelligence] defined purely by behaviour in an environment, or by the mechanisms that arrive at that behaviour?&quot;

This is important because Google just gave control over data center cooling to an AI.  Here it is clearly the mechanism itself that demonstrates utility, but if we call that mechanism intelligent, for intelligence to have meaning, we still have to contend with &quot;intelligent how?&quot;  (In what way is it intelligent?) If we want to know &quot;how intelligent?&quot; (its degree of utility) we still have to evaluate its performance in relation to the performance of other mechanisms.
(In the case of the automata controlling the air conditioning at Google, we can say that it is more intelligent than the prior control system, and by how much.)
Because we're starting to talk about more &quot;generalized intelligence&quot;, defined here as mechanisms that can be applied to a set of problems, (I include minimax as a form of &quot;axiomatic intelligence&quot; and machine learning as a form &quot;adaptive intelligence&quot;), it may be worthwhile to expand and clarify the definition:

Intelligence is the problem solving strength of a mechanism in relation to a problem or a set of problems, relative to the strength of other mechanisms.

or, if we wanted to be pithy:

Intelligence is as intelligence does (and how well.)